53 citations · 124 across the 21 of their papers we have counts for
11 papers · 1 filter
Thick morphisms, higher Koszul brackets, and -algebroids
Hovhannes Khudaverdian, Theodore Voronov
It is a classical fact in Poisson geometry that the cotangent bundle of a Poisson manifold has the structure of a Lie algebroid. Manifestations of this structure are the Lichnerowi…
Operator pencils on the algebra of densities
A. Biggs, H. M. Khudaverdian
In this paper we continue to study equivariant pencil liftings and differential operators on the algebra of densities. We emphasize the role that the geometry of the extended manif…
Geometry of differential operators of second order, the algebra of densities, and groupoids
H. M. Khudaverdian, Th. Th. Voronov
In our previous works, we introduced, for each (super)manifold, a commutative algebra of densities. It is endowed with a natural invariant scalar product. In this paper, we study g…
Differential forms and odd symplectic geometry
Hovhannes M. Khudaverdian, Theodore Th. Voronov
We recall the main facts about the odd Laplacian acting on half-densities on an odd symplectic manifold and discuss a homological interpretation for it suggested recently by P. {Š}…
Geometry of differential operators, odd Laplacians, and homotopy algebras
Hovhannes Khudaverdian, Theodore Voronov
We give a complete description of differential operators generating a given bracket. In particular we consider the case of Jacobi-type identities for odd operators and brackets. Th…
Berezinians, Exterior Powers and Recurrent Sequences
H. M. Khudaverdian, Th. Th. Voronov
We study power expansions of the characteristic function of a linear operator in a -dimensional superspace . We show that traces of exterior powers of satisfy unive…
Laplacians in Odd Symplectic Geometry
Hovhannes M. Khudaverdian
We consider odd Laplace operators arising in odd symplectic geometry. Approach based on semidensities (densities of weight 1/2) is developed. The role of semidensities in the Batal…
On odd Laplace operators. II
Hovhannes M. Khudaverdian, Theodore Voronov
We analyze geometry of the second order differential operators, having in mind applications to Batalin--Vilkovisky formalism in quantum field theory. As we show, an exhaustive pict…
On odd Laplace operators
Hovhannes M. Khudaverdian, Theodore Voronov
We consider odd Laplace operators acting on densities of various weight on an odd Poisson (= Schouten) manifold . We prove that the case of densities of weight 1/2 (half-densiti…
On complexes related with calculus of variations
Hovhannes Khudaverdian, Theodore Voronov
We consider the variational complex on infinite jet space and the complex of variational derivatives for Lagrangians of multidimensional paths and study relations between them. The…
Semidensities on Odd Symplectic Supermanifolds
Hovhannes Khudaverdian
We consider semidensities on a supermanifold E with an odd symplectic structure. We define a new -operator action on semidensities as the proper framework for Batalin-Vilkovisky…